Coefficient of variation

[Derek in NYC]

I use Statking (Conjelco) to record my results. One output is called c.v., which I think stands for coefficient of variation. Can anybody explain in idiot-speak what this means, and how it is different from standard deviation? Also, what is desirable, bigger or smaller?

[Siegmund]

Coefficient of variation = standard deviation / mean.

In the 'real world' it's used mostly for variables which are always positive (dividing by zero is a bad thing), and mostly for things where the uncertainty is proportional to the value of the variable.

In poker, we usually standardize both the mean and the standard deviation by dividing by the big bet, instead of using the c.v. much. It does have a couple of theoretical uses: size of bankroll needed is proportional to CV, and expected time until showing a profit to CV^2.

[BruceZ]

[ QUOTE ]
Coefficient of variation = standard deviation / mean.

In the 'real world' it's used mostly for variables which are always positive (dividing by zero is a bad thing), and mostly for things where the uncertainty is proportional to the value of the variable.

In poker, we usually standardize both the mean and the standard deviation by dividing by the big bet, instead of using the c.v. much. It does have a couple of theoretical uses: size of bankroll needed is proportional to CV, and expected time until showing a profit to CV^2.

[/ QUOTE ]

Bankroll needed is proportional to variance/mean, not SD/mean. bankroll formulas (http://archiveserver.twoplustwo.com/showflat.php?Cat=&Number=207100&page=&view=&sb=5&o =&fpart=all&vc=1) and derivation of bankroll formulas (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=683150&page=0&view=ex panded&sb=5&o=14&fpart=2#Post682045683150).

[RacersEdge]

As a side note, in process improvement CV is used to describe the variability of a process. Typically a CV of 1 is an "average" varying process. A CV of 2 or higher is considered a tough process to control easily. I would imagine poker is way up over 2. (Not sure what the units are here - BB/hr?)

[chris_a]

CV is an interesting statistic.

Facts about CV:

-CV is unitless, that's right, it has no units
-CV depends on the length of the session, for instance I have a 0.025BB/hand EV at 0.5/1.0 Party Poker and a 1.35BB/hand Std. Dev. That means my CV for one hand is 1.35/0.025 = 54. However, over 100 hands, my EV is 2.5BB/100 hands and my Std. Dev. is 13.5 BB/100 hands. Thus my CV is 5.4 over 100 hands. Thus CV goes down for longer sessions.
-CV for a certain length session can tell you your chances of being up after a certain length session.
-CV smaller is better

Possibly more to come soon. /images/graemlins/smile.gif